A three-dimensional finite element code is used for the eigenvalue analysis of the thermoacoustic combustion instabilities modeled through the Helmholtz equation. A full annular combustion chamber, equipped with several burners, is examined. Spatial distributions for the heat release intensity and for the time delay are used for the linear flame model. Burners, connecting the plenum and the chamber, are modeled by means of the transfer matrix method. The influence of the parameters characterizing the burners and the flame on the stability levels of each mode of the system is investigated. The obtained results show the influence of the 3D distribution of the flame on the modes. Additionally, the results show what types of modes are most likely to yield humming in an annular combustion chamber. The proposed methodology is intended to be a practical tool for the interpretation of the thermoacoustic phenomenon (in terms of modes, frequencies, and stability maps) both in the design stage and in the check stage of gas turbine combustion chambers.